Alex's Aces

Alexander picks an integer $ k $ in the range [1,52][1, 52]. Then, he draws the first $ k $ cards from a standard, shuffled 52-card deck. Alexander wins a prize if the last card he draws is an ace and if there exists exactly one ace in the remaining cards. What value of $ k $ should Alexander choose to maximize his chances of winning the prize?

Answer format: enter an integer.